groupBLASSO: Group Bayesian Lasso

In abnormally-distributed/Bayezilla: Bayesian Models With JAGS and Several Utilities for Data Exploration and Model Evaluation.

Description

Group selection was introduced in the group LASSO by Yuan and Lin (2006) in the context of the classical "frequentist" LASSO. The concept is adapted here to the Bayesian LASSO following the example of Kyung et al. (2010)

Note that for the binomial and poisson likelihood functions the New Bayesian LASSO is adapted for use here, which utilizes a scale mixture of uniform distributions to obtain the Laplacian priors (Mallick & Yi, 2014). I have found that this parameterization simply samples faster for the binomial and poisson models, but is logically equivalent to the normal-exponential mixture parameterization. Plug-in pseudovariances are used for these.

Usage

groupBLASSO(X, y, idx, family = "gaussian", log_lik = FALSE,
  iter = 10000, warmup = 1000, adapt = 2000, chains = 4,
  thin = 1, method = "parallel", cl = makeCluster(2), ...)

Arguments

X	the model matrix. Construct this manually with model.matrix()[,-1]
y	the outcome variable
idx	the group labels. Should be of length = to ncol(model.matrix()[,-1]) with the group assignments for each covariate. Please ensure that you start numbering with 1, and not 0.
family	one of "gaussian", "binomial", or "poisson".
log_lik	Should the log likelihood be monitored? The default is FALSE.
iter	How many post-warmup samples? Defaults to 10000.
warmup	How many warmup samples? Defaults to 1000.
adapt	How many adaptation steps? Defaults to 2000.
chains	How many chains? Defaults to 4.
thin	Thinning interval. Defaults to 1.
method	Defaults to "parallel". For an alternative parallel option, choose "rjparallel" or. Otherwise, "rjags" (single core run).
cl	Use parallel::makeCluster(# clusters) to specify clusters for the parallel methods. Defaults to two cores.
...	Other arguments to run.jags.

Details

Model Specification:



Plugin Pseudo-Variances:

Value

a runjags object

References

Yuan, Ming; Lin, Yi (2006). Model Selection and Estimation in Regression with Grouped Variables. Journal of the Royal Statistical Society. Series B (statistical Methodology). Wiley. 68 (1): 49–67. doi:10.1111/j.1467-9868.2005.00532.x

Park, T., & Casella, G. (2008). The Bayesian Lasso. Journal of the American Statistical Association, 103(482), 681-686. Retrieved from http://www.jstor.org/stable/27640090

Kyung, M., Gill, J., Ghosh, M., and Casella, G. (2010). Penalized regression, standard errors, and bayesian lassos. Bayesian Analysis, 5(2):369–411.

Mallick, H., & Yi, N. (2014). A New Bayesian Lasso. Statistics and its interface, 7(4), 571–582. doi:10.4310/SII.2014.v7.n4.a12

Examples

groupBLASSO()

abnormally-distributed/Bayezilla documentation built on Oct. 31, 2019, 1:57 a.m.